Combine the pumpkin puree, egg, salt, and nutmeg in a mixing bowl. Stir in the flour gradually until a soft dough forms.
Turn the dough onto a floured surface and knead briefly until smooth. Divide into four pieces and roll each into a rope about 3/4 inch thick.
Cut the ropes into 1-inch pieces. Place the pieces on a floured baking sheet and set aside.
Bring a large pot of salted water to a boil. Add the gnocchi in batches and cook until they float to the top, about 2 to 3 minutes. Remove with a slotted spoon and set aside.
Melt the butter in a large skillet over medium heat. Continue cooking until the butter turns golden brown and smells nutty.
Add the sage leaves to the browned butter and cook for 1 minute until crisp. Return the cooked gnocchi to the skillet and toss gently to coat.
Remove from heat and stir in the Parmesan cheese. Season with black pepper before serving.